New York — There was a certain wistfulness to President Obama’s eighth and final appearance on the "Late Show with David Letterman." Perhaps it’s because both men, both a bit grayer over the years, are on the runway toward retirement.

Mr. Letterman’s last show, after 33 years as a late night TV host, is May 20. Mr. Obama has 20 months left as president, but as the race to replace him gears up, he is increasingly seen as a lame duck. Inevitably, the talk turned to post-retirement plans.

“Well, I was thinking you and me, we could play some dominoes together,” Obama told Letterman Monday. “We can, you know, go to the local Starbucks and swap stories.”

“Are you kidding me, after eight years of this you’re only taking a month off?” Letterman said.

Obama replied that he and his wife, Michelle, plan to stay involved in issues – helping young people find opportunity, helping military families, “issues like climate change, which are generational challenges.” He also encourages young people to get involved in politics.

But “I really like the idea of playing dominoes with you,” Obama said.

“I know you think I’m no good at dominoes … but I’m pretty good at dominoes. And I plan to teach law at Columbia,” Letterman deadpanned.

“That’s good,” Obama, the former law professor, laughed. “I’d be interested in sitting in on that class. That would be a hoot.”

Despite moments of levity, most of Obama’s appearance centered on serious issues – about the violence in Baltimore and other cities, free trade, racism, and the Obama project that seems especially near to his heart, My Brother’s Keeper. Earlier in the day, Obama had unveiled a new private-sector nonprofit, the My Brother’s Keeper Alliance, which will work to support boys and young men of color in leading productive lives.

My Brother’s Keeper seems destined to be a major focus of Obama’s post-presidency. When he spoke at a roundtable discussion on the initiative Monday afternoon at Lehman College, then in public remarks, Obama spoke in unusually personal terms – as he has done in the past when speaking of the challenges faced by minority youth.

He spoke of growing up without a dad and feeling lost, and how he was given second and third chances when some young men today aren’t afforded that opportunity. Through education and mentoring, My Brother’s Keeper aims to break the school-to-prison pipeline endemic to some urban areas.

“This will remain a mission for me and for Michelle not just for the rest of my presidency, but for the rest of my life,” Obama said at Lehman College in the Bronx.

Obama went straight from that speech to the Letterman taping at the Ed Sullivan Theater in Manhattan, and so the post-presidency talk perhaps wasn’t driven solely by Letterman’s own impending retirement.

But even as both men expressed mutual admiration in the president’s final appearance on the show, they also kept the quips coming.

“Let me ask you, is this the first country you've presidented?” Letterman asked, a reprise of No. 9 on his Top 10 List, “Questions Dumb Guys Ask the President.”

“It is, I suspect, the first and last country I'm presidenting,” Obama replied. “Unlike late night talk-show hosts, I'm term limited.”

In case you’re not sure, that was a joke. Every year, a team of writers come up with the president’s annual correspondents’ dinner speech, often funnier than the actual comedian hired to perform at the event.

And for the record, here’s the full Top 10 List of “Questions Dumb Guys Ask the President”:

10. What do I know you from?
9. Is this the first country you’ve presidented?
8. Who appoints the first lady?
7. Have you met Iron Man?
6. Will you show us your birth certificate?
5. If it's the Secret Service, why have I heard of it?
4. May I have a Dakota?
3. When will we end our dependence on foreign Vergaras?
2. Will you be a guest on one of my last shows? 1. When will you return my gyrocopter?